Connect hair particle to emitter mesh
Well, I finally found what goes wrong. It's simply due to the particle settings: I checked "B-spline" in the "render" section, which interpolate hairs shape using B-spline, and induce a shift between the root vertice of hair and its actual rendered root.



I thought using this setting be useful to have smooth shaped hairs, but in fact using "Curve segment primitive" (Cycles Hair Rendering panel) is sufficient and works great !